A High-Efficiency Class-E Power Amplifier withWide-Range Load in WPT Systems

Shuangke Liu, Ming Liu, Minfan Fu, Chengbin Ma and Xinen Zhu*University of Michigan-Shanghai Jiao Tong University Joint Institute

Shanghai Jiao Tong University, Shanghai, China 200240

Abstract—A high-efficiency power amplifier (PA) is importantin a Megahertz wireless power transfer (WPT) system. It isattractive to apply the Class-E PA for its simple structure andhigh efficiency. However, the conventional design for Class-E PAcan only ensure a high efficiency for a fixed load. It is necessaryto develop a high-efficiency Class-E PA for a wide-range load inWPT systems. A novel design method for Class-E PA is proposedto achieve this objective in this paper. The PA achieves highefficiency, above 80%, for a load ranging from 10 to 100 Ω at6.78 MHz in the experiment.

Index Terms—Wireless power transfer, Class-E power ampli-fier, wide-range load, load-pull, impedance transformation

I. INTRODUCTION

WIRELESS power transfer (WPT) makes it possible forpeople to get rid of messy wires, providing great

convenience for users. It can have larger spatial freedom byincreasing the system frequency to Megahertz [1], enablingconcurrent charging for multiple devices. Usually, such asystem is driven by a power amplifier (PA). One significantchallenge for the WPT systems is the load variation for PA,which is mainly caused by the changes of coils’ positions orthe number of loads. For example, in [2], the load seen byPA increases as the number of charging devices increases.Based on such a system, it is promising that the PA canprovide increasing output power with the increase of PA’s load.Therefore, it is necessary to develop a reliable power amplifier,which can provide adequate power with high efficiency for awide-range load.

The Class-E PA is first introduced by Sokal and Sokal in1975 [3]. It is attractive to be used in MHz WPT system forits high efficiency and simple structure [4], [5]. The Class-EPA achieves high efficiency, approaching 100% theoretically,when the circuit satisfies zero voltage switching (ZVS) condi-tion and zero voltage derivative (ZDS) condition [6]. However,the design is only valid for a fixed load. The efficiency de-creases quickly once the load deviates from the optimal valueand the output power is not proportional to the load. In [7], [8],fixed circuit components are replaced by tunable componentsto increase the PA efficiency when the load of PA varies.However, it requires additional tuning, detection, and controlcircuits, which inevitably increases the system complexity.This paper proposes an approach to design a high-efficiencyClass-E PA by optimizing the circuit structure and parameters.No control system is required. The efficiency keeps high for awide-range load and the output power increases with the load

Lf

Cs

jXC0L0

VDD

RlS

resonant circuit

(a) (b)

Rl (Ohm)

0

20

16

12

8

4

100%

80%

60%

40%

20%

0 100806040200

P0 (W) Efficiency

P0

PDC

Fig. 1. Basic Class-E power amplifier. (a) Topology of Class-E PA. (b) Theoutput power and efficiency for different Rl.

of PA increasing. It is believed that this PA is suitable for highfrequency WPT applications, especially for those systems withmultiple charging devices.

In this paper, a novel design method is proposed to designa high-efficiency Class-E PA working in a wide load range.In Section II, a traditional design for Class-E PA is given andthe requirements for PA design are presented. Then in SectionIII, the circuit tuning methods and impedance transformationnetwork are presented to achieve the objectives based onsimulations. Finally, the proposed design method is validatedin the experiment in section IV.

II. CLASS E POWER AMPLIFIER ANALYSIS

Fig. 1 (a) shows a general circuit configuration of a Class-EPA. It consists of a DC supply VDD, a RF choke Lf , a switchS, a shunt capacitor CS , a series resonant circuit L0C0, a purereactance jX and a load Rl. P0 is the output power of PAand PDC is the input power of DC supply. The PA efficiencyequals to the ratio of P0 and PDC . In order to maximize thePA efficiency, Rl, CS and X are determined by the followingequations (1) - (3), which have been proposed by [6].

Rl =8

π2 + 4· V

2DD

P0≈ 0.5768

V 2DD

P0(1)

CS =8

ωπ(π2 + 4)Rl≈ 0.1836

ωRl(2)

X =π(π2 − 4)

16Rl ≈ 1.1525Rl (3)

A simulation is set up according to Fig. 1 (a). ChooseVDD = 20 V, P0 = 19.2 W and set the operation frequency6.78 MHz. The circuit parameters are derived from (1) - (3).

The model of SUD06N10 (N-Channel MOSFET) is used andthe inductors and capacitors are ideal in the simulation. Fig. 1(b) shows the output power and efficiency for different Rl.This PA can only work efficiently within a narrow load rangeand the output power is not proportional to Rl.

This PA is further analyzed by the load-pull simulation andthe results are illustrated on a Smith chart (see Fig. 2). Theconstant efficiency contours and output power contours aregiven to provide a overview of PA performance for arbitraryload. The load variation line presents Rl varying from 1to 100 Ω. Only a small section of this line locates withinhigh efficiency region and the load variation line have twointersection points with some constant output power contours,which are consistent with the results of Fig. 1 (b). If all theloads for PA locates within the high efficiency region, theefficiency will keep high for all these loads. If the all the loadsfor PA constitute a load variation line, which has no morethan one intersection point with each constant power contourand the load increases along the direction of output powerincreasing, the output power will increase monotonically asthe load increases. So a impedance transformation network isrequired to transform Rl to the desired region.

96.8%

94.8%

92.8%

1.7W21.7W

41.7W

Line 1

constant power contour

load variation line of Rl

Rl increasing

constant efficiency contour

Rl increasing

Fig. 2. Constant contours on the Smith chart.

Lf

Cs

jX

Rl

C0L 0

VDD

resonant circuit

Z in

S

impedance

transformation

Fig. 3. The Class-E PA with impedance transformation network

As is shown Fig. 3, the input impedance Zin is the equiv-alent load for Class-E PA and it depends on Rl. If all theZin locate within the high efficiency region, the PA efficiencywill keep high for a wide-range Rl. If all the Zin forms aload variation line like Line 1 in Fig. 2, along which the

corresponding Rl increases, the output power will increasemonotonically as Rl increases.

The objective of PA design in this paper is to achieve high-efficiency power delivering when Rl varies in a wide range andrealize increasing output power with increasing Rl. In orderto achieve these goals, two steps are required to achieve thisobjective:

1) Find a line located within the high efficiency region andhaving the characteristics of Line 1 by tuning CS .

2) Design a impedance transformation network to make theload variation line of Zin match the line obtained formstep 1 as much as possible.

III. SYSTEM REALIZATION

A. Tuning the shunt capacitor CS

After numerous simulations and comparisons, it is noticedthat CS is the most suitable to modulate the constant contoursand the line satisfying the requirements. As is shown in Fig 4,the high efficiency region expands and the desired line rotatesclockwise when CS decreases. The output power for the loadwithin high efficiency region decreases. In this paper, CS isset to be 180 pF and Line 2 in Fig. 5 is selected as the idealload variation line.

21.7W

1.7W

92.8%

4.1W13.3W

93.3%

5.3W

20.1W

93.6%

(a) (b) (c)

constant power contour constant efficiency contour

Fig. 4. Constant contours for different CS . (a) CS = 358.7pF. (b) S = 180pF. (c) CS = 60 pF.

B. Impedance Transformation

The Π topology is widely used for impedance transfor-mation and it can satisfy the requirements of impedancetransformation in this paper. The topology of Π network isshown in Fig. 6 (a). The target of the network design is tomake the load variation line of Zin match Line 2 in Fig. 5 asmuch as possible.

Line 2 can be represented by: Γimag = 1.86Γreal + 1,Γreal ∈ (−0.7, 0), Γimag ∈ (−0.3, 1). For the fixed X1, X2

and X3, the reflection coefficient ΓZ of Zin depends on Rl

and the relationship between ΓZ,imag and ΓZ,real is obtained.X1, X2 and X3 should ensure that the relationship betweenΓZ,imag and ΓZ,real approximates the representation of Line2 as much as possible when Rl varying from 1 to 100 Ω. Thenumerical method can provide a prediction for X1, X2 andX3. Further modulation by manual are necessary to ensurethe load variation line match Line 2 as much as possible. Inthis paper, X1, X2, X3 are set to be −j37, j27.2 and −j75.7,respectively.

Rl increasing

96.8%

Line 3Line 2

36.1W

20.1W

4.1W

constant power contour

constant efficiency contour

92.8%

load variation line of Zin

Fig. 5. Constant contours after tuning CS . Line 2: the ideal load variationline. Line 3: the load variation line for Zin.

0 20 40 60 80 1000

5

10

15

20

25

30

35

30%

40%

50%

60%

70%

80%

90%

100%

Rl (Ohm)

P0 (W) Efficiency

jX2

jX3 jX1 RlZin

(a) (b)

Fig. 6. Adding a Π network. (a) The topology of Π network. (b) The PAperformance with Π network.

Line 3 in Fig. 5 is the load variation line of Zin. It locateswithin the high efficiency region and along it the output powerincreases with the increase of Rl. The PA performance for thefinal system is depicted in Fig. 6 (b). The efficiency keeps highfor the load varying in a wide range and the output power isapproximately proportional to Rl.

IV. EXPERIMENTAL VERIFICATION

The proposed Class-E PA is fabricated on a FR-4 substratewith thickness of 1.6 mm. The prototype of the fabricatedClass-E PA is illustrated in Fig 7. SUD06N10 is used andoperates as a switch. The value of components on the board isillustrated in Table I. The driving circuit provides a 6.78 MHzsquare wave as the driving signal with 50% duty ratio andamplitude of 5 V. VDD is set to be 20 V in the experiment. Thetest results are shown in Fig 8. The efficiency is not as highas that in the simulation because of the parasitic resistance incircuit. The experiment validates the feasibility of this designmethod: high efficiency for a wide-range load and increasingoutput power with increasing load.

V. CONCLUSION

In this paper a novel design method is proposed to designa high-efficiency Class-E PA working in a wide load range.The design bases on load-pull technique and impedance trans-formation technique. As a result, the output power of Class-E

SUD06N10L1 C1

DC input

Driving circuit

Impedance

transformation network

L2

C3

C2

Cs

Power resistor

Fig. 7. The prototype of the fabricated Class-E PA

Cs CsL1 C1 L2 C2 C3

(before tune) (after tune)

340pF 180pF 2.62µH 240pF 820nH 490pF310pF

TABLE I

The value for each component on the board

50%

90%

80%

70%

60%

100%

Rl (Ohm)

60 1004020 800

12

9

6

3

0

15

P0 (W) Efficiency

P

Efficiency

50%

90%

80%

70%

60%

100%

Rl (Ohm)

60 1004020 800

20

15

10

5

0

25

P0 (W) Efficiency

P

Efficiency

(a) (b)

Fig. 8. Measurement results. (a) Measurement results for traditional Class-EPA. (b) Measurement results for Class-E PA based on the design method ofthis paper.

power amplifier is approximately proportional to the load andthe efficiency keeps high even when the load varies in a widerange.

REFERENCES

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[3] N. O. Sokal and A. D. Sokal, “Class e - a new class of high-efficiencytuned single-ended switching power amplifiers,” Solid-State Circuits,IEEE Journal of, vol. 10, no. 3, pp. 168–176, 1975.

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[5] W. Chen, R. Chinga, S. Yoshida, J. Lin, C. Chen, and W. Lo, “A 25.6w 13.56 mhz wireless power transfer system with a 94% efficiency ganclass-e power amplifier,” in Microwave Symposium Digest (MTT), 2012IEEE MTT-S International. IEEE, 2012, pp. 1–3.

[6] M. Albulet, RF power amplifiers. SciTech Publishing, 2001.[7] S. Aldhaher, P. C. Luk, and J. F. Whidborne, “Wireless power transfer

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